Question: What do the following two equations represent? $3x-4y = -3$ $6x-8y = -1$
Solution: Putting the first equation in $y = mx + b$ form gives: $3x-4y = -3$ $-4y = -3x-3$ $y = \dfrac{3}{4}x + \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $6x-8y = -1$ $-8y = -6x-1$ $y = \dfrac{3}{4}x + \dfrac{1}{8}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.